The present invention relates to medical imaging and, more particularly, to a method of deconvolving an ultrasonic echo sequence, and to an ultrasound imaging apparatus that employs this method.
Because of the coherence of the back-scattered echo signals, images obtained from echo ultrasound imaging systems have extremely complex patterns that bear no obvious relationship to the macroscopic properties of the insonified object. The vast majority of biological tissues are extremely small on the scale of an acoustic wavelength. Consequently, a signal obtained within a resolution cell consists of contributions of many independent scatterers. Interference of these de-phased echoes gives rise to a pattern that has the appearance of a chaotic jumble of “speckles”, known as speckle noise. The speckle pattern consists of a multitude of bright spots where the interference is highly constructive, dark spots where the interference is destructive, and brightness levels between these extremes. The presence of speckle noise in an ultrasound image reduces the ability of a user to resolve fine details. Speckle noise obscures very small structures, for example, early stage tumors, and decreases the reliability of tissue characterization. Therefore, the suppression of speckle noise is an important component of medical ultrasound imaging.
For the purpose of modeling the interaction of biological tissue with ultrasonic waves, the biological tissue is considered to be an assembly of reflectors and scatterers. A reflector is a plane interface that is large compared to the wavelength and that reflects portions of the transmitted energy back towards the transmitter. A scatterer is an object that is small compared to the wavelength and that scatters the transmitted signal in all directions. Such a system often is modeled as a (most generally 3D) function called the spatial response of insonified material, the reflectivity function, or (in medical applications) the spatial tissue response.
An ultrasound radio frequency (RF) image can be considered to consist of 1D echo sequences, also known as “RF lines”. Assuming the tissue properties to be uniform in the plane perpendicular to the scanning beam, an acquired 2D RF image can be viewed as the result of the convolution of the 2D reflectivity function (which accounts for inhomogeneity in the scanning plane) and the 2D transducer point spread function (PSF). Thus, the RF image can be considered to be a distorted version of the true reflectivity function, where the distorting kernel is the transducer PSF. This distortion includes the speckle noise discussed above.
In principle, it should be possible to measure the PSF in a calibration procedure, and then to deconvolve the PSF from the RF image. In practice, however, this is not possible, for several reasons. Perhaps the most important reason is that the absorption of ultrasound energy in tissues increases with frequency. This frequency-dependent attenuation causes both the PSF amplitude and the PSF shape to depend on depth in the tissue, leading to the observed non-stationarity of RF sequences.
In medical ultrasound, a pulse is transmitted into the tissue to be imaged, and the echoes that are backscattered to the emitting transducer are detected as a voltage trace RF line. The RF line conventionally is modeled as being a convolution of a hypothetical 1D PSF with a hypothetical 1D tissue reflectivity function. Assuming that the scatterers on each image line are located on a uniform grid and that the system impulse response is range shift invariant along each image line, a discretized version of the received signal can be written as:rf[n]=a[n]*s[n]+noise[n]  (1)where n is a time index, rf[n] is the RF line, s[n] is the transmitted ultrasound PSF, a[n] is a reflectivity sequence corresponding to the reflectivity function, noise[n] is measurement noise, and “*” represents convolution. Because the frequency-dependent attenuation process appears as a decrease with distance of the mean frequency and amplitude of the PSF, it is commonly assumed that the received echo signal may be expressed as a depth-dependent PSF convolved with the tissue reflectivity function. To make the PSF “location dependent”, s[n] in equation (1) is replaced by s[n,k], where k is the location index. This leads to the observed non-stationarity of the RF lines received from the tissue. In order to deal with this non-stationarity, the RF-sequence is broken up into a number of possibly overlapping segments, such that within each segment the frequency-dependent attenuation process can be ignored and equation (1) holds. The problem of tissue characterization is thus reduced to a set of blind deconvolution problems: for each segment of a given RF line, the respective ultrasonic PSF should be estimated and removed.
To this end, homomorphic signal processing has been applied to rf[n]. Ignoring the noise term on the right hand side of equation (1) for now, transforming equation (1) to the frequency domain gives:RF(w)=A(w)S(w)  (2)i.e., in the frequency domain, the frequency spectrum A(w) of the reflectivity sequence is multiplied by the frequency spectrum S(w) of the PSF to give the frequency spectrum RF(w) of the echo sequence. These spectra can be written asRF(w)=|RF(w)|ej·arg(RF(w))  (3)A(w)=|A(w)|ej·arg(A(w))  (4)S(w)=|S(w)|ej·arg(S(w))  (5)Taking the complex logarithm of both sides of equation (2) then giveslog|RF(w)|=log|A(w)|+log|S(w)|  (6)arg[RF(w)]=arg[A(w)]+arg[S(w)]  (7)
As described in the Annexes, the log spectrum of the echo sequence, log|RF(w)|, thus is a sum of a smooth and regular log spectrum, log|S(w)|, of the PSF and a jagged and irregular log spectrum, log|A(w)|, of the reflectivity sequence. Cepstrum-based techniques have been used to exploit the qualitatively different natures of the PSF and reflectivity log spectra to isolate the PSF log spectrum for the purpose of estimating the PSF and deconvolving the estimated PSF from the echo sequence. See, for example, Torfinn Taxt, “Restoration of medical ultrasound images using two-dimensional homomorphic deconvolution”, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 42 no. 4 pp. 543-554 (July 1995); Torfinn Taxt, “Comparison of cepstrum-based methods for radial blind deconvolution of ultrasound images”, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 44 no. 3 pp. 666-674 (May 1997); J. A. Jensen and S. Leeman, “Nonparametric estimation of ultrasound pulses”, IEEE Transactions on Biomedical Engineering, vol. 41 pp. 929-936 (1994); and J. A. Jensen, “Deconvolution of ultrasound images”, Ultrasonic Imaging, vol. 14 pp. 1-15 (1992). Cepstrum-based techniques, however, suffer from certain limitations, as discussed in Annex A. Briefly, the complex cepstrum of a signal of finite duration has been shown to extend to infinity. This invariably leads to aliasing errors when the Discrete Fourier Transform or a similar discrete numerical method is used to compute the cepstrum.
There is thus a widely recognized need for, and it would be highly advantageous to have, a method of estimating an ultrasound PSF that would overcome the disadvantages of presently known methods as described above.